Martingale transforms on Banach function spaces

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5 Citations (Scopus)

Abstract

We establish the boundedness of martingale transforms on Banach function spaces by using the Rubio de Francia extrapolation theory and the interpolation theorem by Zygmund. The main result also yields the boundedness of the martingale transforms on rearrangement-invariant Banach function spaces, Orlicz spaces, Lorentz-Karamata spaces, Zygmund spaces, Lebesgue spaces with variable exponents, Morrey spaces with variable exponents and Lorentz-Karamata Morrey spaces. Copyright © 2022 the Author(s), licensee AIMS Press.

Original languageEnglish
Pages (from-to)2247-2262
JournalElectronic Research Archive
Volume30
Issue number6
DOIs
Publication statusPublished - Apr 2022

Citation

Ho, K.-P. (2022). Martingale transforms on Banach function spaces. Electronic Research Archive, 30(6), 2247-2262. doi: 10.3934/era.2022114

Keywords

  • Martingale transform
  • Banach function spaces
  • Orlicz spaces
  • Lorentz-Karamata spaces
  • Variable Lebesgue spaces
  • Morrey spaces

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